PLL Algorithms: All 21 Cases

PLL means permutation of the last layer: once the top face is all yellow, one PLL algorithm moves the top pieces into their right places and the cube is solved (sometimes with one last turn of the top). There are 21 cases, each with a letter name. The arrows show where pieces travel when you do the moves.

Two-look PLL: first fix the corners with an A perm (or a T perm), then fix the edges with a U perm, H perm or Z perm. That is just six algorithms to start with.

Corners only

Aa perm

x R' U R' D2 R U' R' D2 R2 x'

Ab perm

x R2 D2 R U R' D2 R U' R x'

E perm

x' R U' R' D R U R' D' R U R' D R U' R' D' x

Edges only

H perm

M2 U M2 U2 M2 U M2

Ua perm

M2 U M U2 M' U M2

Ub perm

M2 U' M U2 M' U' M2

Z perm

M' U M2 U M2 U M' U2 M2

Swap two corners and two edges

T perm

R U R' U' R' F R2 U' R' U' R U R' F'

Ja perm

x R2 F R F' R U2 r' U r U2 x'

Jb perm

R U R' F' R U R' U' R' F R2 U' R'

F perm

R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R

Ra perm

R U' R' U' R U R D R' U' R D' R' U2 R'

Rb perm

R' U2 R U2 R' F R U R' U' R' F' R2

Swap corners across and two edges

V perm

R' U R' U' y R' F' R2 U' R' U R' F R F

Y perm

F R U' R' U' R U R' F' R U R' U' R' F R F'

Na perm

R U R' U R U R' F' R U R' U' R' F R2 U' R' U2 R U' R'

Nb perm

R' U R U' R' F' U' F R U R' F R' F' R U' R

Three corners and three edges

Ga perm

R2 U R' U R' U' R U' R2 U' D R' U R D'

Gb perm

R' U' R U D' R2 U R' U R U' R U' R2 D

Gc perm

R2 U' R U' R U R' U R2 U D' R U' R' D

Gd perm

R U R' U' D R2 U' R U' R' U R' U R2 D'

Watch the T perm

R U R' U' R' F R2 U' R' U' R U R' F'

The T perm swaps two corners and two edges. It is often the first full PLL people learn.

In these algorithms, x and y turn the whole cube, M is the middle slice and r turns two layers. See notation if any letters are new.

Questions people ask

Which PLL should I learn first?

The T perm and the two U perms are a good start, followed by the A perms. Together they cover two-look PLL with the H and Z perms.

Why does the cube need a last top turn after some PLLs?

Some algorithms finish with the top layer turned a quarter or half turn away from solved. One U, U’ or U2 lines it up. Cubers call this AUF (adjust upper face).